Is there a method to align 3D cursor's axes with selected vertecies?
This sounds needlessly complex. This problem can be solved with moving a point on the line and selecting it when it is needed.
You want the cursor on any point P on given line L.

in vertex select mode , select line
right click &gt; subdivide line, you will have point P now.
move point P by pressing g twice , this will move it along the line (And make the line yellow), place this on the line where you need the cursor to go. If you need exact number you can use .5 and -.5 to go 1/4 or 3/4 of the way on the line from the middle.
Shift +S snap cursor to selected
(optional) select point P , then one of your line vertices, F3&gt; Merge &gt; at Last , this will merge your vertex in when you are done with it.

If you need other &quot;imaginary lines&quot; you can use this method , build temporary (2 verts then f ) lines, and then delete the temporary lines when you are done lining up things.